Constructive drawing by Hanstein Herman

Author:Hanstein, Herman. [from old catalog]
Language: eng
Format: epub, pdf
Tags: Mechanical drawing
Publisher: Chicago, New York [etc.] Keuffel & Esser co.
Published: 1908-03-25T05:00:00+00:00

Fig. 4.

Fi.c:. 2.

Fig. 5.

Plate 15

Fig. 3.

Pig- 6

Hansteln's Constructive Drawing.

62.— Fig. 1.— Problem.— To construct a line equal to the semi-circumference of a given circle.

Solution. —In the given circle C draw two perpendicular diameters, A B and F G, and, at G, the indefinite line E H perpendicular to F G. With A as center and A C as radius describe arc C D and draw line ODE. Make E 3 = 3 A C and draw F 3 = G H, which is equal to the semi-circumference of the circle C. Calculation gives—

F 3 = 8.14153 times radius; error = 0.00006 of semi-circumference. Denoting the ratio of the circumference to the diameter of a circle by the letter tt, then this ratio has been more accurately found to be

IT = 3.1415926; for common usage it suffices to take for it— ■7T = V = 3.14:28, with an error = 0.001. Among the many approximative methods to rectify a circle, the above method has the advantage that it can be performed with one opening of the compasses.

TANGENTS.

63.— Fig. 2.— Problem. — To construct a tangent at a given point of a circle.

Definition. —A tangent is a line touching the circumference of a circle in one point only, the point of contact, and is a perpendicular to a radius, drawn to the point of contact.

Solution. —Let C be the given circle and A the point of contact. Draw the radius C A, and perpendicular to it, at point A, the line M N, which is the required tangent.

64.— Fig. 3.— Problem. — From a given point outside a circle to draw tangents to this circle.

Solution. —Let C be the given circle and A the outside point. Draw A C, and on A C as a diameter describe a circle, center B; this circle B intersects circle G at points O and P; then lines A O and A P are tangents to circle C.

65.— Fig. 4.— Problem. — To construct common exterior tangents to two given circles. Solution. —Let C and A be the given circles. Draw line C A and upon this as diameter, circle C A; with the difference C F, of the radii D A and C E draw are H P I from center C, intersecting circle B at points H and I. Draw radius C O through H, and OP through I. Radii AO' and AP' are parallel to CO and CP respectively. O'O and P'P are the points of contact of the common tangents.

66.— Fig. 5.—Problem. — To construct common interior tangents to two circles.

Solution.—Follow the previous construction and describe the circle C F A G. With the sum of the radii of both circles AD + CI = CE draw arc PEG; also the lines C P and its parallel radius A P', and C G and its parallel A O'. The intersections O and O', P and P' are the points of contact of the required tangents P P' and O O'.

Fig. 1.

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